Path-time independent trajectory planning of ladder climbing with shortest path length for a four-limbed robot

This paper describes a trajectory planning method of ladder climbing for a four-limbed robot. The overall design of the four-limbed robot and the specific design of its end-effector is explained. The trajectory planning consists of two components: path planning and time planning, and the separation of these two parts are realized by arc-length parameterization. In path planning, we use cubic spline interpolation to generate the path according to the given mid-points. It is a fact that the shape of path depends on the choice of the coefficients of the interpolation polynomial, and so does the path length. Therefore, we propose a minimization of path length so that once the mid-points are all given, the generated path will always be the shortest spline curve. For time planning, it enables us to decide how long the path goes in arbitrary given times. Due to the independence between path and time planning, different time planning along the same path can be applied for the purpose of speed adjustment, avoidance of moving obstacles, releasing the burden of motors and so on. Results from simulations and experiments authenticate the validity of our trajectory planning method.